Two simple

Two simple fractions have the product of 3/10. When the smaller fraction is divided by the bigger fraction, the quotient is 5/6. What are the two fractions in simplest form?

Correct answer:

a =  3/5
b =  1/2

Step-by-step explanation:

$$\begin{gathered} a\cdot b=\frac{3}{10} \\ b/a=5/6 \\ a\cdot (5/6\cdot a)\cdot 3/10 \\ {a}^2=3/10\cdot 6/5 \\ a=\sqrt{3/10\cdot 6/5}=\frac{3}{5}=0.6 \end{gathered}$$

$$\begin{gathered} b=5/6\cdot a=5/6\cdot 0.6=\frac{1}{2}=0.5 \\ \text{ Verifying Solution: } \\ p=a\cdot b=0.6\cdot 0.5=\frac{3}{10}=0.3 \\ d=b/a=0.5/0.6=\frac{5}{6}\doteq 0.8333 \end{gathered}$$

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